Advertisements
Advertisements
प्रश्न
A 100 µF capacitor in series with a 40 Ω resistance is connected to a 110 V, 60 Hz supply.
(a) What is the maximum current in the circuit?
(b) What is the time lag between the current maximum and the voltage maximum?
Advertisements
उत्तर
Capacitance of the capacitor, C = 100 μF = 100 × 10−6 F
Resistance of the resistor, R = 40 Ω
Supply voltage, V = 110 V
(a) Frequency of oscillations, v = 60 Hz
Angular frequency, ω = 2πv = 2π × 60 rad/s
For an RC circuit, we have the relation for impedance as:
Z = `"R"^2 + 1/(ω^2"C"^2)`
Peak voltage, V0 = `"V"sqrt2 = 110 sqrt2 "V"`
Maximum current is given as:
I0 = `"V"_0/"Z"`
= `"V"_0/sqrt("R"^2 + 1/(ω^2"C"^2))`
= `(110 sqrt2)/sqrt((40)^2 + 1/((120π)^2 xx (10^-4)^2))`
= `(110 sqrt2)/sqrt(1600 + 10^8/(120π)^2)`
= 3.24 A
(b) In a capacitor circuit, the voltage lags behind the current by a phase angle of Φ. This angle is given by the relation:
∴ `tan phi = (1/(ω"C"))/"R" = 1/(ω"CR")`
= `1/(120π xx 10^-4 xx 10)`
= 0.6635
`phi` = tan−1 (0.6635) = 33.56°
= `(33.56π)/180 "rad"`
∴ Time lag = `phi/ω`
= `(33.56π)/(180 xx 120π)`
= 1.55 × 10−3 s
= 1.55 ms
Hence, the time lag between maximum current and maximum voltage is 1.55 ms.
APPEARS IN
संबंधित प्रश्न
An inductor coil of some resistance is connected to an AC source. Which of the following quantities have zero average value over a cycle?
(a) Current
(b) Induced emf in the inductor
(c) Joule heat
(d) Magnetic energy stored in the inductor
An inductance of 2.0 H, a capacitance of 18μF and a resistance of 10 kΩ is connected to an AC source of 20 V with adjustable frequency.
(a) What frequency should be chosen to maximize the current in the circuit?
(b) What is the value of this maximum current?
An applied voltage signal consists of a superposition of a dc voltage and an ac voltage of high frequency. The circuit consists of an inductor and a capacitor in series. Show that the dc signal will appear across C and the ac signal across L.
A current of 4A flows in a coil when connected to a 12V dc source. If the same coil is connected to a 12V, 50 rad/s a.c. source, a current of 2.4A flows in the circuit. Determine the inductance of the coil.
An inductive circuit contains resistance of 10 ohms and an inductance of 2 henry. If an A.C. voltage of 120 Volts and frequency 60 Hz is applied to this circuit, the current would be nearly ______.
An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance ‘R’ are connected in series to an ac source of potential difference ‘V’ volts as shown in the figure.
The potential difference across L, C, and R is 40 V, 10 V and 40 V, respectively. The amplitude of the current flowing through the LCR series circuit is `10sqrt2 "A"`. The impedance of the circuit is:
Explain why the reactance offered by an inductor increases with increasing frequency of an alternating voltage.
An electrical device draws 2kW power from AC mains (voltage 223V (rms) = `sqrt(50,000)` V). The current differs (lags) in phase by `phi(tan phi = (-3)/4)` as compared to voltage. Find (i) R, (ii) XC – XL, and (iii) IM. Another device has twice the values for R, XC and XL. How are the answers affected?
An ideal inductor is connected across an AC source of voltage. The current in the circuit ______.
Draw a phasor diagram showing e and i in the case of a purely inductive circuit. A 40-turn square coil of side 0.2 m is placed in a magnetic field of induction 0.05 T with the plane of the coil perpendicular to the direction of the field. If the magnetic induction is uniformly reduced to zero in 5 milliseconds, find the emf induced in the coil.
The magnetic potential energy stored in a certain inductor is 25 mJ, when the current in the inductor is 60 mA. This inductor is of inductance ______.
A 2 mH inductor is connected to 220 V, 50 Hz AC (X1) and then to DC (X2). Find X1 and X2.
The inductive reactance XL of a purely inductive circuit is given by ______.
